Respuesta :

[tex]\mleft[\mleft(2x\mright)^x\mleft(2x\mright)^{2x}\mright]^{\frac{1}{x}}[/tex]

We have the expression above

we will use two of the laws of exponents in order to simplify the expression

[tex]x^m\cdot x^n=x^{m+n}[/tex][tex](x^m)^n=x^{m\cdot n}[/tex]

using these two laws we will have

[tex]\begin{gathered} \lbrack(2x)^x(2x)^{2x}\rbrack^{\frac{1}{x}}=\lbrack(2x)^{x+2x}\rbrack^{\frac{1}{x}}=\lbrack(2x)^{3x}\rbrack^{\frac{1}{x}}=(2x)^{3x\cdot\frac{1}{x}}=(2x)^3=2^3x^3 \\ =8x^3 \end{gathered}[/tex]

the simplification is

[tex]\lbrack(2x)^x(2x)^{2x}\rbrack^{\frac{1}{x}}=8x^3[/tex]